Theres a lot to unpack, especially with all the unecessary video posts.
"On the crash - the comment by B0OM is helpful. One question I would add: given how common you say the situation is, is there a risk of alarm fatigue with the stick shaker? How often in a pilot's career might they have the shaker activate? And what does the stall recovery procedure say to do with the flaps?"
I'd honestly say I don't know (or have seen or meet) an ATR pilot who is unaware the stick shaker has activated. It's a rather intense shaker and if crews are capable and trained correctly the muscle memory should take over and they will push. Regarding flap selection.......if clean the memo items call for Flap 15 if you have Flap 30 it stays there until the clean up post event.
Reagrding Vmca.......an ATR with an active shaker or pusher will go off well before Vmca is reached in a single engine situation. In fact to get the machine to perform (demo) the Vmca you have to deactivate the shaker and pusher and take it almost to the point of stalling. Apart from demonstration in a sim during training I have never witnessed a crew get even close to Vmca.
To the comments regarding tail plane ice. My understanding is the flight was conducted in VMC and there was no icing. If there was icing and it was bad enough to develop tail plane icing the crew would have encountered severe ice and therefore the SEV ICE memo items and checklist. That checklist limits flap to 15 for approach and landing which increases your approach speed significantly and then another factor is applied meaning you'll get nowhere near your stall speed (comment: no ATR crew in their right mind would do a circling approach after a severe icing event unless there was no other option anywhere).
If as someone suggested the ground speed was around 92 knots, this ATR was unbeliveably slow for a flap 30 config, let alone a flap 15 config. Conservative manoeuvring speeds for the ATR are 180 KIAS clean, 150 KIAS Flap 15 and Gear and 130 KIAS Flap 30. Minimum speed is 95 KCAS (period) and you'll only get close to this on an empty aircraft with no wind. The Yeti aircraft was pretty full, some basic math.............ATR empty weight 13800 kg (with crew), 68 pax with bags = 6800 kg so ZFW = 20600 kg (only 2400 kg away from MTOW if it was the 23000 kg variant). I don't know the fuel they had on board so lets just say they had a landing weight of 21000 kg. Below is the base performance data
VmHB 30 (Vref) = 107 kts
Correction = 1/3 headwind or all of the gust and that will give the Vapp. Most airlines use a stabilsation criteria of Vapp 0 - +10 some use 0 - +20
Vs Flap 30 and Gear down at 21000kg is approximately 87 Kcas
Vs Flap 15 and Gear UP at 21000kg is approximately 97 Kcas
As you may or may not see ATR gives crews approximately a 1.23 buffer (23%) Vref over Vs, its concievable if you have a 10 knot headwind that the Vapp will increase to 110 KIAS moving you further from stalling.